Q1
i.
Draw an expiry payoff (not a profit) diagram illustrating the trading strategy. Diagrams
must be annotated with axis names and strike prices.
For the purpose of drawing an expiry trade-off, we need to plot the diagram based on the prices
and the premiums of the options. We already have the information that K1< K2<K3<K4. Let us
assume the value of given option as K1 =$60, K2=$80, K3=$100 and K4=$120, with the current
strike price of $90.
Let us assume the premium as
Call Options – Buys at $60
Premium Paid -
-$25
Call Option- Sells at $80
Premium Received
Buys at $120
-$3
Sells at $100
$14
$6
The table for the various strike price would be
Strike Price
Call at $60
Call at $80
Call at $100
Call at $120
50
$-25
$14
$6
$-3
60
$-25
$14
$6
$-3
70
$-15
$14
$6
$-3
80
$-5
$14
$6
$-3
90
$5
$4
$6
$-3
100
$15
$-6
$6
$-3
110
$20
$-16
$-4
$-3
120
$25
$-26
$-14
$-3
130
$35
$-36
$-24
$7
140
$45
$-46
$-34
$17
expiry tradeoff
$80.00
$60.00
$40.00
P
a
y
o
f
f
s
$20.00
$-
$-20.00
$-40.00
$-60.00
1
2
3
4
5
call at $60
$-25.
$-25.
$-15.
$-5.0
put at $80
$14.0 $14.0 $14.0 $14.0 $4.00
6
7
8
9
10
$5.00 $15.0 $25.0 $35.0 $45.0 $55.0
$-16.
$-26.
$-36.
$-46.
put at $100 $6.00 $6.00 $6.00 $6.00 $6.00 $6.00 $-4.0
$-14.
$-24.
$-34.
Call at $120 $-3.0
$-3.0
$7.00 $17.0
$-3.0
$-3.0
$-3.0
$-3.0
$-6.0
$-3.0
$-3.0
The expiry trade off diagram given above explains the trading strategy. If the strike price of the
call option goes up buyer of a call option makes the profit which is shown in the diagram by blue
line and violet lines and seller of the call option incurs loss as the strike price goes up which is
shown in the graph by red and green lines. This can also be explained by the diagram given
below:
ii.
What is the lower boundary for the value of the trading strategy?
Maximum profit for a buyer of an option is unlimited and maximum loss is the premium paid to
buy the option. And maximum profit for seller of an option is the premium which he/she receives
and maximum loss for seller of an option can be unlimited.
The formula to calculate the lower boundary of the call option is given below:
C = E (ST) – X
Here
C = Value of the call option
E (ST) = Expected value of the asset at time T
X = Strike Price
For example if the expected value of the asset is $ 100 for the call option of strike price $60 then
the value of the option will be $ 100 - $ 60 = $ 40, therefore the profit is $ 15 as the premium paid
is $ 25.
For the call option bought at $60, the maximum loss or the lower boundary could be the amount
of premium paid i.e. $ 25.
For the call option sold at $80, the potential loss could be unlimited and would start increasing,
once the price of the option crosses the strike price of the put.
For the call option sold at $100, again the potential of loss could be unlimited.
For the call option bought at $120, again the lower boundary for the option would be the amount
of premium paid.
iii.
What is the upper boundary for the value of the trading strategy?
Value of the call option of strike price $ 80 at expected value of asset of $ 100 will be $ 20 but the
premium received is $ 14 therefore there is a loss of $ 6.
For the call option bought at $60,the upper boundary for gain could be the difference between the
strike price and the exercise price. The potential for gain in this case would be unlimited.
For the put option sold at $80, the potential for gain would be the amount of premium received.
For the put option sold at $100, also the potential for gain would be the amount of premium
received.
For the call option bought at $120, there could be a potential for unlimited gain. The upper
boundary could be the difference between the strike price and the exercise price. (Cohen 2005)
Q2
i.
Draw an expiry payoff (not a profit) diagram illustrating the trading strategy. Diagrams
must be annotated with axis names and strike prices.
In this case, the assumptions would be
sells an European put option at K1 =$60
buys European call option at K2 =$80,
current strike price of $90.
Again, it is assumed that premium is paid at $6 on call option and received at $3 on put option.
Expiry trade offs
$40.00
$30.00
Payoffs
$20.00
$10.00
$$-10.00
$-20.00
$-30.00
$-40.00
1
2
3
4
5
6
7
8
9
10
put at $60 $-27 $-17 $-7. $3.0 $3.0 $3.0 $3.0 $3.0 $3.0 $3.0
Call at $80 $-6.
$-6.
$-6.
$-6.
$-6.
$-6. $4.0 $14. $24. $34.
The trading strategy of the option can be explained by the diagram given below:
As the strike price of a put option goes down the buyer of a put option makes profit which is
shown in the expiry trade off diagram by blue line for a put option of strike price $ 60. Also a call
option is taken in the strategy to minimize the loss from put option if the strike price goes up.
ii.
What is the lower boundary for the value of the trading strategy?
A buyer of a put option can make unlimited profit and the loss could be only the premium paid to
purchase the put option. Also the seller of a put option can make only limited profit which is
premium received.
Value of a put option can be determined by the difference between the strike price and the
expected value of the underlying asset. The formula is given below:
P = X - E (ST)
Here
P = value of the put option
X = strike price
E (ST) = expected value of the underlying asset
With the help of the value of the option we can calculate the upper and lower boundary of the
option.
For the call option bought at $80, the maximum loss or the lower boundary could be the amount
of premium paid.
For the put option sold at $60, the potential loss could be unlimited and would start increasing,
once the price of the option crosses the strike price of the put.
iii.
What is the upper boundary for the value of the trading strategy?
For the call option bought at $80,the upper boundary for gain could be the difference between the
strike price and the exercise price. The potential for gain in this case would be unlimited.
For the put option sold at $60, the potential for gain would be the amount of premium received.
Question 3
i. Draw an expiry payoff (not a profit) diagram illustrating the trading strategy. Diagrams must
be annotated with axis names and strike prices.
Solution:
In this case, the trader
buys put option at $60,
buys call option at $100 and
sells put option at $80,
current strike at $90.
Further, it is assumed that premium is paid at
$3when buying put option at $60,
$7 on call option at $100 and
received premium at $4 on selling put option at $80.
Expiry Trade offs
$40.00
$30.00
$20.00
Payoffs
$10.00
$$-10.00
$-20.00
$-30.00
1
2
3
4
5
6
7
8
9
10
put at $60
$7.0
$-3.
$-3.
$-3.
$-3.
$-3.
$-3.
$-3.
$-3.
$-3.
Call at $100
$-7.
$-7.
$-7.
$-7.
$-7.
$-7.
$3.0
$13.
$23.
$33.
put at $80
$-26 $-16
$-6.
$4.0
$4.0
$4.0
$4.0
$4.0
$4.0
$4.0
The diagram given above explains the strategy that the trader bought one put and one call option
and sold one put option. The loss which is made by put at $ 60 is compensated by the call at $
100.
ii.
What is the lower boundary for the value of the trading strategy?
As explained above the lower and upper boundary of the options can be calculated according to
the nature of the option that is whether trader is a buyer of the option or seller of the option.
For the put option bought at $60, the maximum loss or the lower boundary could be the amount of
premium paid.
For the call option bought at $100, the lower boundary would be the amount of premium paid.
For the put option sold at $80, the potential loss could be unlimited and would start increasing,
once the price of the option falls below the strike price of the put option.
iii.
What is the upper boundary for the value of the trading strategy?
For the put option bought at $60,the upper boundary for gain could be the difference between the
strike price and the exercise price. The potential for gain in this case would be unlimited.
For the call option bought at $100, the upper boundary for gain could be the difference between
the strike price and the exercise price. The potential for gain in this case would be unlimited.
For the put option sold at $80, the potential for gain would be the amount of premium received.
Bibliography
Cohen, Guy. The Bible of Options Strategies: The Definitive Guide for Practical Trading Strategies.
Prentice Hall, 2005.